Preliminary results
Data description
setwd("~/Documents/LSHTMproject/Rcode")
load("LCA.Rdata")
library(epiDisplay)
library(plyr)
library(tidyverse)
library(poLCA)
# Number of subjects per survey year
with(NDNS, tab1(SurveyYear, graph = FALSE, decimal = 2))## SurveyYear :
## Frequency Percent Cum. percent
## NDNS Year 1 801 13.01 13.01
## NDNS Year 2 812 13.19 26.21
## NDNS Year 3 782 12.71 38.91
## NDNS Year 4 1055 17.14 56.05
## NDNS Year 5 625 10.15 66.21
## NDNS Year 6 663 10.77 76.98
## NDNS Year 7 703 11.42 88.40
## NDNS Year 8 714 11.60 100.00
## Total 6155 100.00 100.00# Number of subjects per servey year by gender where Men == 1, Women == 2
with(NDNS, tabpct(SurveyYear, Sex, graph = FALSE, decimal = 2))##
## Original table
## Sex
## SurveyYear 1 2 Total
## NDNS Year 1 336 465 801
## NDNS Year 2 350 462 812
## NDNS Year 3 339 443 782
## NDNS Year 4 418 637 1055
## NDNS Year 5 249 376 625
## NDNS Year 6 254 409 663
## NDNS Year 7 321 382 703
## NDNS Year 8 270 444 714
## Total 2537 3618 6155
##
## Row percent
## Sex
## SurveyYear 1 2 Total
## NDNS Year 1 336 465 801
## (41.9) (58.1) (100)
## NDNS Year 2 350 462 812
## (43.1) (56.9) (100)
## NDNS Year 3 339 443 782
## (43.4) (56.6) (100)
## NDNS Year 4 418 637 1055
## (39.6) (60.4) (100)
## NDNS Year 5 249 376 625
## (39.8) (60.2) (100)
## NDNS Year 6 254 409 663
## (38.3) (61.7) (100)
## NDNS Year 7 321 382 703
## (45.7) (54.3) (100)
## NDNS Year 8 270 444 714
## (37.8) (62.2) (100)
##
## Column percent
## Sex
## SurveyYear 1 % 2 %
## NDNS Year 1 336 (13.24) 465 (12.85)
## NDNS Year 2 350 (13.80) 462 (12.77)
## NDNS Year 3 339 (13.36) 443 (12.24)
## NDNS Year 4 418 (16.48) 637 (17.61)
## NDNS Year 5 249 (9.81) 376 (10.39)
## NDNS Year 6 254 (10.01) 409 (11.30)
## NDNS Year 7 321 (12.65) 382 (10.56)
## NDNS Year 8 270 (10.64) 444 (12.27)
## Total 2537 (100) 3618 (100)# summary of their age
NDNS %>%
group_by(SurveyYear, Sex) %>%
summarise(N = n(), MeanAge = mean(Age), SDAge = sd(Age), minAge = min(Age), maxAge = max(Age))## # A tibble: 16 x 7
## # Groups: SurveyYear [?]
## SurveyYear Sex N MeanAge SDAge minAge maxAge
## <chr> <chr> <int> <dbl> <dbl> <dbl> <dbl>
## 1 NDNS Year 1 1 336 49.9 17.3 19 86
## 2 NDNS Year 1 2 465 49.2 17.8 19 94
## 3 NDNS Year 2 1 350 48.9 17.3 19 96
## 4 NDNS Year 2 2 462 50.2 17.9 19 92
## 5 NDNS Year 3 1 339 48.5 16.9 19 87
## 6 NDNS Year 3 2 443 49.6 18.0 19 93
## 7 NDNS Year 4 1 418 51.4 17.0 19 90
## 8 NDNS Year 4 2 637 48.8 17.0 19 94
## 9 NDNS Year 5 1 249 51.7 16.6 19 93
## 10 NDNS Year 5 2 376 49.4 17.8 19 92
## 11 NDNS Year 6 1 254 51.1 17.7 19 93
## 12 NDNS Year 6 2 409 49.0 18.1 19 95
## 13 NDNS Year 7 1 321 51.5 18.3 19 92
## 14 NDNS Year 7 2 382 49.8 18.3 19 89
## 15 NDNS Year 8 1 270 50.4 16.8 19 90
## 16 NDNS Year 8 2 444 49.9 17.7 19 94# Dietary data by day
vecid1<-unique(dta_day1$id) # n = 6153
vecid2<-unique(dta_day2$id) # n = 6153
vecid3<-unique(dta_day3$id) # n = 6151
vecid4<-unique(dta_day4$id) # n = 6026
setdiff(vecid, vecid1) # two subjects did not have day 1 data## [1] 50506161 70908241setdiff(vecid, vecid2) # two subjects did not have day 2 data## [1] 31012251 40714261setdiff(vecid, vecid3) # four subjects did not have day 3 data## [1] 10914251 11205071 80702191 81210131setdiff(vecid, vecid4) # 129 subjects did not have day 4 data## [1] 10112011 10701161 10702161 10707261 10906181 10910111 10914251
## [8] 20106041 20116171 20202081 20205081 20301211 20307041 20405101
## [15] 20509211 20602011 20615041 21002101 21011041 21107031 21113041
## [22] 21211041 21211101 30113231 30205131 30205201 30402131 30404081
## [29] 30411081 30417081 30603071 30605131 30609131 30708201 30709031
## [36] 30906071 30906201 30907251 30912021 31110201 40101011 40104021
## [43] 40109221 40116011 40214081 40221221 40315101 40402221 40410251
## [50] 40504211 40506221 40516021 40710081 40710101 40714251 40714261
## [57] 40803081 40803221 40808081 40814131 40816011 40902051 40904021
## [64] 41012081 41016131 41202051 50104191 50105161 50306241 50310271
## [71] 50501271 50504271 50710161 51002141 51002191 51004011 51102241
## [78] 51203191 51205141 51208041 51209071 60202081 60202261 60206161
## [85] 60310131 60313021 60405161 60508071 60606271 60808161 60909271
## [92] 61013261 61102251 61109081 70113191 70302241 70305031 70309241
## [99] 70311181 70311251 70407251 70613181 70703181 70714181 70802241
## [106] 70812251 70815241 71101061 71206191 80108061 80301061 80301281
## [113] 80302191 80308251 80312241 80405181 80405281 80410131 80611131
## [120] 80713281 80805191 81002251 81004251 81005191 81007061 81101221
## [127] 81110061 81110131 81203221day 1 data (3 classes)
# LCA in day1 -------------------------------------------------------------
# noquote(paste(rep("H", 24), 0:23, sep = ""))
#H0 H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 H13 H14 H15 H16 H17 H18 H19 H20 H21 H22 H23
f <- cbind(H0, H1, H2, H3, H4, H5, H6, H7, H8, H9, H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21,H22,H23) ~ 1
lc3 <- poLCA(f, dta_d1_wide, nclass = 3, graphs = TRUE, maxiter = 10000)
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $H0
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0008 0.0088 0.0052 0.9853
## class 2: 0.0003 0.0103 0.0067 0.9827
## class 3: 0.0429 0.0566 0.0028 0.8978
##
## $H1
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0075 0.0021 0.9904
## class 2: 0.0000 0.0026 0.0045 0.9929
## class 3: 0.0142 0.0210 0.0043 0.9605
##
## $H2
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0040 0.0028 0.9932
## class 2: 0.0000 0.0015 0.0026 0.9959
## class 3: 0.0103 0.0065 0.0017 0.9814
##
## $H3
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0035 0.0045 0.9920
## class 2: 0.0000 0.0005 0.0028 0.9967
## class 3: 0.0078 0.0064 0.0000 0.9858
##
## $H4
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0004 0.0080 0.0043 0.9873
## class 2: 0.0000 0.0033 0.0024 0.9942
## class 3: 0.0088 0.0062 0.0021 0.9828
##
## $H5
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0001 0.0144 0.0082 0.9772
## class 2: 0.0011 0.0080 0.0047 0.9862
## class 3: 0.0063 0.0076 0.0050 0.9810
##
## $H6
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0125 0.0896 0.0496 0.8483
## class 2: 0.0131 0.0718 0.0312 0.8839
## class 3: 0.0377 0.1171 0.0279 0.8173
##
## $H7
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0078 0.1996 0.1135 0.6790
## class 2: 0.0168 0.2212 0.1131 0.6488
## class 3: 0.0334 0.1689 0.0572 0.7405
##
## $H8
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0214 0.2383 0.1254 0.6149
## class 2: 0.0205 0.2472 0.1447 0.5876
## class 3: 0.0599 0.2562 0.0775 0.6063
##
## $H9
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0093 0.2087 0.0985 0.6835
## class 2: 0.0096 0.2228 0.1097 0.6579
## class 3: 0.0546 0.2483 0.0832 0.6139
##
## $H10
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0125 0.2298 0.1152 0.6425
## class 2: 0.0139 0.2616 0.1228 0.6017
## class 3: 0.0610 0.2755 0.0643 0.5992
##
## $H11
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0130 0.1524 0.0842 0.7504
## class 2: 0.0108 0.2041 0.0968 0.6882
## class 3: 0.0655 0.2294 0.0731 0.6320
##
## $H12
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0542 0.5103 0.0924 0.3431
## class 2: 0.0094 0.1012 0.0440 0.8454
## class 3: 0.0599 0.2691 0.0712 0.5998
##
## $H13
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0021 0.0264 0.0539 0.9176
## class 2: 0.0764 0.8092 0.1144 0.0000
## class 3: 0.0920 0.2995 0.0408 0.5677
##
## $H14
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0153 0.2544 0.0717 0.6587
## class 2: 0.0010 0.0799 0.0556 0.8635
## class 3: 0.0872 0.2539 0.0692 0.5897
##
## $H15
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0172 0.2245 0.1004 0.6579
## class 2: 0.0133 0.2127 0.1096 0.6643
## class 3: 0.1038 0.1829 0.0639 0.6493
##
## $H16
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0195 0.2016 0.0718 0.7071
## class 2: 0.0212 0.2017 0.0961 0.6810
## class 3: 0.0992 0.2214 0.0690 0.6104
##
## $H17
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0416 0.2539 0.0509 0.6537
## class 2: 0.0324 0.2211 0.0546 0.6918
## class 3: 0.0888 0.2344 0.0412 0.6356
##
## $H18
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0407 0.3341 0.0516 0.5736
## class 2: 0.0642 0.3476 0.0469 0.5413
## class 3: 0.1420 0.1863 0.0318 0.6400
##
## $H19
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0418 0.2486 0.0607 0.6489
## class 2: 0.0637 0.2761 0.0555 0.6047
## class 3: 0.1974 0.2652 0.0115 0.5259
##
## $H20
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0320 0.2446 0.0771 0.6463
## class 2: 0.0497 0.2495 0.0701 0.6307
## class 3: 0.2720 0.2362 0.0247 0.4670
##
## $H21
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0330 0.2388 0.0819 0.6464
## class 2: 0.0444 0.2366 0.0940 0.6250
## class 3: 0.2768 0.1542 0.0135 0.5555
##
## $H22
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0168 0.1411 0.0552 0.7869
## class 2: 0.0260 0.1551 0.0620 0.7569
## class 3: 0.2027 0.1783 0.0319 0.5871
##
## $H23
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0021 0.0408 0.0204 0.9366
## class 2: 0.0070 0.0432 0.0210 0.9288
## class 3: 0.0854 0.0974 0.0112 0.8061
##
## Estimated class population shares
## 0.4571 0.4171 0.1258
##
## Predicted class memberships (by modal posterior prob.)
## 0.4635 0.4492 0.0873
##
## =========================================================
## Fit for 3 latent classes:
## =========================================================
## number of observations: 6153
## number of estimated parameters: 218
## residual degrees of freedom: 5935
## maximum log-likelihood: -99389.52
##
## AIC(3): 199215
## BIC(3): 200681
## G^2(3): 92059.43 (Likelihood ratio/deviance statistic)
## X^2(3): 2.789386e+19 (Chi-square goodness of fit)
## # lc3$llik #log-likelihood of model
#
# lc3$P #Estimated class population shares
#
# lc3$predclassday 1 data (Fig.)
Model comparison and selection
| N of classes | N of parameters | G^2 | df | AIC | BIC | log-likelihood |
|---|---|---|---|---|---|---|
| 1 | 72 | 94737.22 | 6081 | 201600.8 | 202085.0 | -100728.40 |
| 2 | 145 | 93030.90 | 6008 | 200040.5 | 201015.6 | -99875.26 |
| 3 | 218 | 92059.43 | 5935 | 199215.0 | 200681.0 | -99389.52 |
| 4 | 291 | 91790.97 | 5862 | 199092.6 | 201049.5 | -99255.29 |
| 5 | 364 | 90721.07 | 5789 | 198168.7 | 200616.5 | -98720.35 |
| 6 | 437 | 90716.77 | 5716 | 198310.4 | 201249.1 | -98718.20 |
| 7 | 510 | 89850.47 | 5643 | 197590.1 | 201019.7 | -98285.04 |
| Note: | ||||||
| Abbreviation: N, number; G^2, the likelihood ratio statistic; df, degree of freedom; AIC, Akaike information criterion; BIC, Bayesian information criterion. |
Five classes visualisation
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $H0
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0021 0.0054 0.0000 0.9925
## class 2: 0.0000 0.0100 0.0070 0.9830
## class 3: 0.0532 0.0733 0.0040 0.8695
## class 4: 0.0036 0.0091 0.0028 0.9845
## class 5: 0.0007 0.0128 0.0095 0.9771
##
## $H1
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0022 0.0025 0.9954
## class 2: 0.0002 0.0025 0.0048 0.9925
## class 3: 0.0197 0.0327 0.0065 0.9411
## class 4: 0.0000 0.0002 0.0024 0.9974
## class 5: 0.0000 0.0116 0.0022 0.9862
##
## $H2
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0000 0.0063 0.9937
## class 2: 0.0000 0.0012 0.0020 0.9968
## class 3: 0.0148 0.0126 0.0014 0.9711
## class 4: 0.0000 0.0013 0.0013 0.9974
## class 5: 0.0000 0.0056 0.0025 0.9919
##
## $H3
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0000 0.0051 0.9949
## class 2: 0.0000 0.0006 0.0025 0.9969
## class 3: 0.0111 0.0123 0.0000 0.9766
## class 4: 0.0000 0.0000 0.0019 0.9981
## class 5: 0.0000 0.0049 0.0050 0.9901
##
## $H4
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0070 0.0037 0.9892
## class 2: 0.0000 0.0031 0.0016 0.9954
## class 3: 0.0112 0.0063 0.0035 0.9789
## class 4: 0.0017 0.0062 0.0011 0.9910
## class 5: 0.0000 0.0078 0.0062 0.9860
##
## $H5
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0191 0.0067 0.9742
## class 2: 0.0009 0.0057 0.0034 0.9900
## class 3: 0.0074 0.0089 0.0000 0.9837
## class 4: 0.0020 0.0133 0.0105 0.9742
## class 5: 0.0000 0.0109 0.0085 0.9807
##
## $H6
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0165 0.1007 0.0441 0.8387
## class 2: 0.0117 0.0706 0.0290 0.8887
## class 3: 0.0380 0.1185 0.0293 0.8141
## class 4: 0.0189 0.0964 0.0433 0.8414
## class 5: 0.0111 0.0755 0.0477 0.8657
##
## $H7
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0082 0.2176 0.0971 0.6772
## class 2: 0.0204 0.2084 0.1070 0.6642
## class 3: 0.0447 0.1450 0.0521 0.7582
## class 4: 0.0038 0.2386 0.1334 0.6241
## class 5: 0.0105 0.1894 0.1093 0.6909
##
## $H8
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0305 0.2721 0.1405 0.5569
## class 2: 0.0195 0.2464 0.1518 0.5822
## class 3: 0.0668 0.2353 0.0782 0.6197
## class 4: 0.0226 0.2457 0.1082 0.6235
## class 5: 0.0192 0.2282 0.1227 0.6300
##
## $H9
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0092 0.2454 0.1016 0.6438
## class 2: 0.0082 0.2149 0.1031 0.6738
## class 3: 0.0670 0.2371 0.0725 0.6234
## class 4: 0.0092 0.2322 0.1207 0.6379
## class 5: 0.0134 0.1957 0.0949 0.6960
##
## $H10
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0248 0.2269 0.1073 0.6410
## class 2: 0.0160 0.2604 0.1194 0.6043
## class 3: 0.0735 0.2676 0.0630 0.5959
## class 4: 0.0123 0.2527 0.1218 0.6132
## class 5: 0.0069 0.2399 0.1155 0.6377
##
## $H11
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0215 0.1406 0.0896 0.7483
## class 2: 0.0113 0.2225 0.1042 0.6619
## class 3: 0.0683 0.2132 0.0787 0.6397
## class 4: 0.0167 0.1906 0.0878 0.7049
## class 5: 0.0106 0.1515 0.0730 0.7649
##
## $H12
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0608 0.5624 0.0904 0.2864
## class 2: 0.0005 0.0084 0.0287 0.9624
## class 3: 0.0607 0.2361 0.0814 0.6218
## class 4: 0.0464 0.3944 0.0740 0.4852
## class 5: 0.0462 0.4569 0.0951 0.4017
##
## $H13
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0104 0.1541 0.0683 0.7673
## class 2: 0.0796 0.8172 0.1031 0.0000
## class 3: 0.0972 0.2881 0.0425 0.5723
## class 4: 0.0390 0.3254 0.0803 0.5552
## class 5: 0.0121 0.1281 0.0643 0.7955
##
## $H14
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0145 0.2177 0.0809 0.6869
## class 2: 0.0000 0.0540 0.0514 0.8946
## class 3: 0.1019 0.2256 0.0739 0.5987
## class 4: 0.0175 0.2410 0.0546 0.6868
## class 5: 0.0142 0.2439 0.0740 0.6679
##
## $H15
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0289 0.2203 0.1158 0.6350
## class 2: 0.0144 0.2149 0.1086 0.6620
## class 3: 0.1167 0.1784 0.0718 0.6331
## class 4: 0.0198 0.2140 0.0985 0.6677
## class 5: 0.0139 0.2222 0.0905 0.6734
##
## $H16
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0082 0.0819 0.0383 0.8716
## class 2: 0.0186 0.1788 0.0912 0.7114
## class 3: 0.1176 0.2152 0.0751 0.5921
## class 4: 0.0363 0.2831 0.1023 0.5783
## class 5: 0.0230 0.2421 0.0834 0.6515
##
## $H17
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.1339 0.7843 0.0817 0.0000
## class 2: 0.0322 0.2292 0.0561 0.6825
## class 3: 0.1027 0.2291 0.0446 0.6236
## class 4: 0.0218 0.1116 0.0435 0.8232
## class 5: 0.0017 0.0296 0.0361 0.9325
##
## $H18
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0086 0.1119 0.0438 0.8357
## class 2: 0.0789 0.3792 0.0485 0.4934
## class 3: 0.1771 0.2042 0.0355 0.5832
## class 4: 0.0202 0.0908 0.0353 0.8536
## class 5: 0.0703 0.5727 0.0593 0.2976
##
## $H19
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0026 0.1315 0.0529 0.8130
## class 2: 0.0587 0.2030 0.0468 0.6914
## class 3: 0.2127 0.1991 0.0098 0.5784
## class 4: 0.1536 0.7661 0.0803 0.0000
## class 5: 0.0186 0.0714 0.0522 0.8577
##
## $H20
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0452 0.2997 0.1045 0.5506
## class 2: 0.0576 0.2598 0.0717 0.6109
## class 3: 0.3185 0.2476 0.0267 0.4073
## class 4: 0.0427 0.1693 0.0443 0.7437
## class 5: 0.0351 0.2518 0.0717 0.6415
##
## $H21
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0285 0.2386 0.0612 0.6717
## class 2: 0.0551 0.2367 0.0918 0.6164
## class 3: 0.3231 0.1423 0.0200 0.5146
## class 4: 0.0536 0.2097 0.0905 0.6461
## class 5: 0.0340 0.2498 0.0836 0.6325
##
## $H22
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0280 0.1609 0.0426 0.7685
## class 2: 0.0295 0.1523 0.0617 0.7565
## class 3: 0.2393 0.1856 0.0266 0.5485
## class 4: 0.0322 0.1407 0.0695 0.7577
## class 5: 0.0144 0.1424 0.0542 0.7890
##
## $H23
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0118 0.0373 0.0152 0.9357
## class 2: 0.0058 0.0431 0.0219 0.9292
## class 3: 0.1033 0.1056 0.0129 0.7782
## class 4: 0.0037 0.0429 0.0234 0.9300
## class 5: 0.0049 0.0478 0.0187 0.9286
##
## Estimated class population shares
## 0.1539 0.2959 0.0876 0.1891 0.2736
##
## Predicted class memberships (by modal posterior prob.)
## 0.155 0.3419 0.066 0.1898 0.2472
##
## =========================================================
## Fit for 5 latent classes:
## =========================================================
## number of observations: 6153
## number of estimated parameters: 364
## residual degrees of freedom: 5789
## maximum log-likelihood: -98768.13
##
## AIC(5): 198264.3
## BIC(5): 200712
## G^2(5): 90816.64 (Likelihood ratio/deviance statistic)
## X^2(5): 2.237912e+18 (Chi-square goodness of fit)
## 
day 2 data (Fig.)
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $H0
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0003 0.0194 0.0041 0.9762
## class 2: 0.0425 0.0321 0.0051 0.9204
## class 3: 0.0000 0.0096 0.0081 0.9822
##
## $H1
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0054 0.0040 0.9907
## class 2: 0.0097 0.0324 0.0021 0.9558
## class 3: 0.0000 0.0005 0.0023 0.9972
##
## $H2
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0018 0.0034 0.9948
## class 2: 0.0179 0.0195 0.0017 0.9608
## class 3: 0.0000 0.0012 0.0013 0.9975
##
## $H3
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0005 0.0033 0.0032 0.9931
## class 2: 0.0032 0.0231 0.0000 0.9736
## class 3: 0.0000 0.0002 0.0025 0.9973
##
## $H4
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0035 0.0035 0.9930
## class 2: 0.0044 0.0132 0.0000 0.9823
## class 3: 0.0004 0.0037 0.0024 0.9934
##
## $H5
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0062 0.0061 0.9877
## class 2: 0.0028 0.0127 0.0087 0.9758
## class 3: 0.0011 0.0107 0.0026 0.9856
##
## $H6
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0147 0.0696 0.0346 0.8811
## class 2: 0.0374 0.0880 0.0128 0.8619
## class 3: 0.0120 0.0871 0.0525 0.8484
##
## $H7
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0098 0.1984 0.1062 0.6856
## class 2: 0.0467 0.1781 0.0739 0.7014
## class 3: 0.0138 0.2201 0.1185 0.6477
##
## $H8
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0178 0.2335 0.1183 0.6304
## class 2: 0.0474 0.2127 0.0648 0.6751
## class 3: 0.0246 0.2599 0.1360 0.5795
##
## $H9
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0098 0.2187 0.1032 0.6683
## class 2: 0.0695 0.2737 0.0967 0.5601
## class 3: 0.0100 0.2135 0.1091 0.6673
##
## $H10
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0191 0.2392 0.1126 0.6291
## class 2: 0.0743 0.2300 0.0740 0.6217
## class 3: 0.0121 0.2446 0.1099 0.6334
##
## $H11
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0135 0.2206 0.0923 0.6736
## class 2: 0.0508 0.2002 0.0619 0.6872
## class 3: 0.0044 0.0981 0.0667 0.8307
##
## $H12
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0103 0.0830 0.0326 0.8740
## class 2: 0.0643 0.2006 0.0467 0.6885
## class 3: 0.0675 0.7961 0.1364 0.0000
##
## $H13
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0480 0.5743 0.0853 0.2925
## class 2: 0.0887 0.3473 0.0778 0.4862
## class 3: 0.0041 0.0202 0.0560 0.9196
##
## $H14
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0175 0.1765 0.0535 0.7524
## class 2: 0.0836 0.2426 0.0583 0.6155
## class 3: 0.0143 0.1731 0.0877 0.7248
##
## $H15
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0134 0.2193 0.0948 0.6725
## class 2: 0.0856 0.1756 0.0473 0.6915
## class 3: 0.0175 0.2161 0.1095 0.6570
##
## $H16
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0156 0.2147 0.0773 0.6924
## class 2: 0.0732 0.1946 0.0789 0.6533
## class 3: 0.0236 0.2021 0.0831 0.6913
##
## $H17
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0280 0.2170 0.0443 0.7107
## class 2: 0.1047 0.1517 0.0632 0.6804
## class 3: 0.0425 0.2785 0.0408 0.6382
##
## $H18
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0430 0.3561 0.0455 0.5554
## class 2: 0.1570 0.2285 0.0317 0.5829
## class 3: 0.0523 0.3156 0.0544 0.5776
##
## $H19
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0428 0.2845 0.0629 0.6098
## class 2: 0.2171 0.2349 0.0342 0.5138
## class 3: 0.0431 0.2400 0.0534 0.6635
##
## $H20
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0321 0.2477 0.0677 0.6525
## class 2: 0.3129 0.2278 0.0307 0.4287
## class 3: 0.0578 0.2462 0.0846 0.6114
##
## $H21
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0358 0.2291 0.0905 0.6446
## class 2: 0.2734 0.1500 0.0031 0.5735
## class 3: 0.0483 0.2194 0.0774 0.6548
##
## $H22
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0214 0.1564 0.0648 0.7574
## class 2: 0.2304 0.1756 0.0297 0.5644
## class 3: 0.0247 0.1317 0.0545 0.7891
##
## $H23
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0013 0.0484 0.0152 0.9352
## class 2: 0.0986 0.0892 0.0052 0.8070
## class 3: 0.0027 0.0349 0.0105 0.9518
##
## Estimated class population shares
## 0.591 0.1178 0.2913
##
## Predicted class memberships (by modal posterior prob.)
## 0.5994 0.0835 0.3171
##
## =========================================================
## Fit for 3 latent classes:
## =========================================================
## number of observations: 6153
## number of estimated parameters: 218
## residual degrees of freedom: 5935
## maximum log-likelihood: -98019.53
##
## AIC(3): 196475.1
## BIC(3): 197941.1
## G^2(3): 89400.39 (Likelihood ratio/deviance statistic)
## X^2(3): 6.215951e+17 (Chi-square goodness of fit)
## 
Model comparison and selection
| N of classes | N of parameters | G^2 | df | AIC | BIC | log-likelihood |
|---|---|---|---|---|---|---|
| 1 | 72 | 92165.61 | 6081 | 198948.3 | 199432.5 | -99402.14 |
| 2 | 145 | 90364.49 | 6008 | 197293.2 | 198268.2 | -98501.58 |
| 3 | 218 | 89311.03 | 5935 | 196385.7 | 197851.7 | -97974.85 |
| 4 | 291 | 88500.33 | 5862 | 195721.0 | 197677.9 | -97569.50 |
| 5 | 364 | 87947.21 | 5789 | 195313.9 | 197761.7 | -97292.94 |
| 6 | 437 | 87351.06 | 5716 | 194863.7 | 197802.4 | -96994.87 |
| 7 | 510 | 86823.89 | 5643 | 194482.6 | 197912.2 | -96731.28 |
| 8 | 583 | 86305.78 | 5570 | 194110.5 | 198031.0 | -96472.23 |
| Note: | ||||||
| Abbreviation: N, number; G^2, the likelihood ratio statistic; df, degree of freedom; AIC, Akaike information criterion; BIC, Bayesian information criterion. |
Four classes visualisation
## Conditional item response (column) probabilities,
## by outcome variable, for each class (row)
##
## $H0
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0007 0.0214 0.0020 0.9760
## class 2: 0.0000 0.0092 0.0033 0.9874
## class 3: 0.0007 0.0186 0.0023 0.9784
## class 4: 0.0576 0.0327 0.0049 0.9048
## class 5: 0.0022 0.0154 0.0306 0.9517
##
## $H1
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0093 0.0041 0.9866
## class 2: 0.0000 0.0000 0.0000 1.0000
## class 3: 0.0000 0.0030 0.0003 0.9967
## class 4: 0.0143 0.0367 0.0033 0.9458
## class 5: 0.0000 0.0032 0.0154 0.9814
##
## $H2
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0025 0.0008 0.9968
## class 2: 0.0000 0.0000 0.0009 0.9991
## class 3: 0.0000 0.0000 0.0036 0.9964
## class 4: 0.0246 0.0211 0.0031 0.9511
## class 5: 0.0016 0.0124 0.0109 0.9751
##
## $H3
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0066 0.0050 0.9884
## class 2: 0.0000 0.0002 0.0016 0.9982
## class 3: 0.0000 0.0000 0.0000 1.0000
## class 4: 0.0043 0.0270 0.0000 0.9688
## class 5: 0.0033 0.0021 0.0048 0.9898
##
## $H4
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0051 0.0022 0.9927
## class 2: 0.0000 0.0033 0.0021 0.9946
## class 3: 0.0000 0.0022 0.0008 0.9970
## class 4: 0.0063 0.0154 0.0000 0.9782
## class 5: 0.0015 0.0041 0.0134 0.9809
##
## $H5
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0000 0.0084 0.0060 0.9856
## class 2: 0.0013 0.0123 0.0000 0.9864
## class 3: 0.0000 0.0037 0.0024 0.9939
## class 4: 0.0041 0.0133 0.0067 0.9759
## class 5: 0.0000 0.0038 0.0231 0.9731
##
## $H6
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0150 0.0840 0.0257 0.8753
## class 2: 0.0128 0.0945 0.0427 0.8499
## class 3: 0.0140 0.0688 0.0309 0.8863
## class 4: 0.0389 0.0899 0.0154 0.8557
## class 5: 0.0197 0.0123 0.0979 0.8700
##
## $H7
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0118 0.2160 0.0823 0.6899
## class 2: 0.0159 0.2380 0.1051 0.6410
## class 3: 0.0139 0.2177 0.1101 0.6583
## class 4: 0.0474 0.1573 0.0815 0.7138
## class 5: 0.0028 0.0601 0.2056 0.7315
##
## $H8
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0188 0.2334 0.1006 0.6472
## class 2: 0.0262 0.2783 0.1265 0.5691
## class 3: 0.0185 0.2809 0.1054 0.5952
## class 4: 0.0558 0.1903 0.0707 0.6832
## class 5: 0.0158 0.0962 0.2198 0.6682
##
## $H9
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0144 0.2266 0.0853 0.6737
## class 2: 0.0125 0.2203 0.0827 0.6845
## class 3: 0.0082 0.2310 0.0757 0.6850
## class 4: 0.0790 0.2717 0.1049 0.5444
## class 5: 0.0063 0.1642 0.2956 0.5339
##
## $H10
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0205 0.2501 0.0860 0.6435
## class 2: 0.0124 0.2616 0.0921 0.6339
## class 3: 0.0254 0.2568 0.1056 0.6122
## class 4: 0.0854 0.2215 0.0824 0.6107
## class 5: 0.0083 0.1196 0.2496 0.6225
##
## $H11
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0159 0.2286 0.0687 0.6867
## class 2: 0.0047 0.1000 0.0439 0.8513
## class 3: 0.0124 0.2364 0.0746 0.6766
## class 4: 0.0641 0.1832 0.0684 0.6843
## class 5: 0.0066 0.1035 0.2516 0.6383
##
## $H12
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0201 0.0954 0.0195 0.8650
## class 2: 0.0740 0.8197 0.1063 0.0000
## class 3: 0.0083 0.1141 0.0289 0.8487
## class 4: 0.0633 0.1898 0.0503 0.6966
## class 5: 0.0085 0.2592 0.2149 0.5174
##
## $H13
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0494 0.5549 0.0722 0.3235
## class 2: 0.0044 0.0000 0.0344 0.9611
## class 3: 0.0581 0.6177 0.0753 0.2489
## class 4: 0.0953 0.3272 0.0856 0.4919
## class 5: 0.0101 0.2897 0.1918 0.5084
##
## $H14
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0161 0.1831 0.0321 0.7687
## class 2: 0.0147 0.1754 0.0677 0.7421
## class 3: 0.0181 0.1706 0.0447 0.7667
## class 4: 0.1030 0.2301 0.0613 0.6057
## class 5: 0.0292 0.1958 0.2189 0.5562
##
## $H15
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0155 0.2053 0.0676 0.7116
## class 2: 0.0195 0.2269 0.0939 0.6597
## class 3: 0.0205 0.2738 0.1027 0.6030
## class 4: 0.0946 0.1725 0.0520 0.6809
## class 5: 0.0067 0.0983 0.2001 0.6948
##
## $H16
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0212 0.2397 0.0573 0.6817
## class 2: 0.0243 0.2036 0.0696 0.7026
## class 3: 0.0129 0.1842 0.0703 0.7326
## class 4: 0.0788 0.1879 0.0887 0.6446
## class 5: 0.0210 0.1830 0.1971 0.5989
##
## $H17
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0350 0.3260 0.0427 0.5963
## class 2: 0.0448 0.2856 0.0332 0.6364
## class 3: 0.0199 0.0403 0.0245 0.9153
## class 4: 0.1247 0.1406 0.0694 0.6653
## class 5: 0.0357 0.2217 0.1172 0.6254
##
## $H18
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0021 0.0530 0.0304 0.9146
## class 2: 0.0560 0.3117 0.0400 0.5923
## class 3: 0.1200 0.8357 0.0443 0.0000
## class 4: 0.1867 0.2050 0.0372 0.5711
## class 5: 0.0278 0.3053 0.1352 0.5318
##
## $H19
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0648 0.4060 0.0526 0.4766
## class 2: 0.0504 0.2399 0.0397 0.6700
## class 3: 0.0284 0.1052 0.0486 0.8178
## class 4: 0.2582 0.2219 0.0324 0.4875
## class 5: 0.0118 0.2322 0.1559 0.6002
##
## $H20
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0390 0.2564 0.0489 0.6558
## class 2: 0.0645 0.2451 0.0688 0.6216
## class 3: 0.0484 0.2253 0.0506 0.6758
## class 4: 0.3646 0.2159 0.0331 0.3864
## class 5: 0.0309 0.2726 0.2087 0.4878
##
## $H21
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0410 0.2404 0.0749 0.6437
## class 2: 0.0524 0.2248 0.0700 0.6528
## class 3: 0.0473 0.2260 0.0840 0.6427
## class 4: 0.3328 0.1457 0.0000 0.5216
## class 5: 0.0298 0.1489 0.1444 0.6769
##
## $H22
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0301 0.1588 0.0428 0.7684
## class 2: 0.0298 0.1305 0.0341 0.8056
## class 3: 0.0277 0.1647 0.0519 0.7558
## class 4: 0.2794 0.1614 0.0345 0.5247
## class 5: 0.0053 0.1405 0.2073 0.6469
##
## $H23
## Low_carb Med_carb High_carb Not_eating
## class 1: 0.0012 0.0450 0.0110 0.9428
## class 2: 0.0039 0.0317 0.0044 0.9600
## class 3: 0.0054 0.0556 0.0094 0.9296
## class 4: 0.1325 0.0944 0.0072 0.7659
## class 5: 0.0000 0.0582 0.0527 0.8891
##
## Estimated class population shares
## 0.35 0.251 0.2237 0.0797 0.0956
##
## Predicted class memberships (by modal posterior prob.)
## 0.3411 0.2891 0.237 0.06 0.0728
##
## =========================================================
## Fit for 5 latent classes:
## =========================================================
## number of observations: 6153
## number of estimated parameters: 364
## residual degrees of freedom: 5789
## maximum log-likelihood: -97273.15
##
## AIC(5): 195274.3
## BIC(5): 197722.1
## G^2(5): 87907.63 (Likelihood ratio/deviance statistic)
## X^2(5): 8.58199e+17 (Chi-square goodness of fit)
## 
